Tight Approximation for Proportional Approval Voting
Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence
Main track. Pages 276-282. https://doi.org/10.24963/ijcai.2020/39
In approval-based multiwinner elections, we are given a set of voters, a set of candidates, and, for each voter, a set of candidates approved by the voter. The goal is to find a committee of size k that maximizes the total utility of the voters. In this paper, we study approximability of Thiele rules, which are known to be NP-hard to solve exactly. We provide a tight polynomial time approximation algorithm for a natural class of geometrically dominant weights that includes such voting rules as Proportional Approval Voting or p-Geometric. The algorithm is relatively simple: first we solve a linear program and then we round a solution by employing a framework called pipage rounding due to Ageev and Sviridenko (2004) and Calinescu et al. (2011). We provide a matching lower bound via a reduction from the Label Cover problem. Moreover, assuming a conjecture called Gap-ETH, we show that better approximation ratio cannot be obtained even in time f(k)*pow(n,o(k)).
Agent-based and Multi-agent Systems: Computational Social Choice
Agent-based and Multi-agent Systems: Voting